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6/28/2017 565320650 1/7 Amplifier Transfer Function Note that the ideal amplifier transfer function: oc vout (t ) = Avo vi (t ) is an equation of a line (with slope = Avo and y -intercept = 0). vout Avo < 0 Avo > 0 vin This ideal transfer function implies that the output voltage can be very large, provided that the gain Avo and the input voltage vin are large. 6/28/2017 565320650 2/7 However, we find in a “real” amplifier that there are limits on how large the output voltage can become. The transfer function of an amplifier is more accurately expressed as: L vout (t ) Avo vin (t ) L vin (t ) Lin Lin vin (t ) Lin vin (t ) Lin This expression is shown graphically as: vout L+ L-in = LAvo L+in Avo L- = L+ Avo vin 6/28/2017 565320650 3/7 * This expression (and graph) shows that electronic amplifiers have a maximum and minimum output voltage (L+ and L-). * If the input voltage is either too large or too small (too negative), then the amplifier output voltage will be equal to either L+ or L- . * If vout = L+ or vout =L- , we say the amplifier is in saturation (or compression). Amplifier saturation occurs when the input voltage is greater than: L vin > + B L+in Avo or when the input voltage is less than: vin L Avo Lin Often, we find that these voltage limits are symmetric, i.e.: L L and Lin Lin For example, the output limits of an amplifier might be L+ = 15 V and L- = -15 V. However, we find that these limits are also often asymmetric (e.g., L+ = +15 V and L- = +5 V). 6/28/2017 565320650 4/7 Q: Why do we care if an amplifier saturates? Does it cause any problems, or otherwise result in performance degradation?? A: Absolutely! If an amplifier saturates—even momentarily— the unavoidable result will be a distorted output signal. For example, consider a case where the input to an amplifier is a triangle wave: vin (t) Lin t Lin 6/28/2017 565320650 5/7 Since Lin vin (t ) Lin for all time t, the output signal will be within the limits L+ and L- for all time t, and thus the amplifier output will be vout (t) = Avo vin (t): vout (t) L t L Consider now the case where the input signal is much larger, such that vin (t ) Lin and vin (t ) Lin for some time t (e.g., the input triangle wave exceeds the voltage limits Lin and Lin some of the time): vin (t) Lin t Lin 6/28/2017 565320650 6/7 This is precisely the situation about which I earlier expressed caution. We now must experience the palpable agony of signal distortion! vout (t) L t L Note that this output signal is not a triangle wave! For time t where vin (t ) Lin and vin (t ) Lin , the value Avo vin (t ) is greater than L+ and less than L-, respectively. Thus, the output voltage is limited to vout (t ) L and vout (t ) L for these times. As a result, we find that output vout (t ) does not equal Avo vin (t ) — the output signal is distorted! 6/28/2017 565320650 7/7 In reality, the saturation voltages L , L , Lin , and Lin are not so precisely defined. The transition from the linear amplifier region to the saturation region is gradual, and cannot be unambiguously defined at a precise point. vout L+ L in L Avo L in L vin Avo Avo Lvout(t) L t L